Null and Alternative Hypotheses for a Mean

The significance level (also known as the "critical value" or "alpha") you should use depends on the costs of different kinds of errors. With a significance level of 0.05, you have a 5% chance of rejecting the null hypothesis, even if it is true. If you try 100 different treatments on your chickens, and none of them really change the sex ratio, 5% of your experiments will give you data that are significantly different from a 1:1 sex ratio, just by chance. In other words, 5% of your experiments will give you a false positive. If you use a higher significance level than the conventional 0.05, such as 0.10, you will increase your chance of a false positive to 0.10 (therefore increasing your chance of an embarrassingly wrong conclusion), but you will also decrease your chance of a false negative (increasing your chance of detecting a subtle effect). If you use a lower significance level than the conventional 0.05, such as 0.01, you decrease your chance of an embarrassing false positive, but you also make it less likely that you'll detect a real deviation from the null hypothesis if there is one.

Support or Reject Null Hypothesis

The test statistic for examining hypotheses about one population mean:

How to Determine a p-Value When Testing a Null Hypothesis

I’m a bit confused too. On my Standard Normal Distribution table, it shows the z-value for 3.41 to be .9997. Where do you get .4997 or .4977- either way I’m not seeing it.

To find thevalue for your test statistic:

Often, the people who claim to avoid hypothesis testing will say something like "the 95% confidence interval of 25.9 to 47.4% does not include 50%, so we conclude that the plant extract significantly changed the sex ratio." This is a clumsy and roundabout form of hypothesis testing, and they might as well admit it and report the P value.

The test statistic for examining hypotheses about one population mean:

hypothesis testing, null hypothesis, P value.

The null hypothesis is a statement that you want to test. In general, the null hypothesis is that things are the same as each other, or the same as a theoretical expectation. For example, if you measure the size of the feet of male and female chickens, the null hypothesis could be that the average foot size in male chickens is the same as the average foot size in female chickens. If you count the number of male and female chickens born to a set of hens, the null hypothesis could be that the ratio of males to females is equal to a theoretical expectation of a 1:1 ratio.

p value and the theory of hypothesis ..

In this example, we are performing an upper tailed test (H1: μ> 191), with a Z test statistic and selected α =0.05. Reject H0 if Z > 1.645.

(b) Which is the p-value of the testing ? What hypothesis must be made for the testing at (a) ?

Since the p-value ll hypothesis with an alpha value of 0.05.

To set up the test, fill in the boxes: What null hypothesis H0 about the mean μ do you want to test? Which alternative hypothesis Ha do you have in mind, and what level of significance α do you require? What value of the standard deviation σ is known to be true? How many observations n will you have (250 or fewer)?

The following figure shows the locations of a test statistic and their corresponding conclusions.

Support or Reject Null Hypothesis in Easy Steps

Notice that the top part of the statistic is the difference between the sample mean and the null hypothesis. The bottom part of the calculation is the standard error of the mean.

Find the probability that  is beyond (more extreme than) your test statistic:

Hypothesis testing - Handbook of Biological Statistics

For (b), make sure you know the definition of a p-value (it's one minus the percentile of your observed test statistic, where the percentile is calculated guessed it...the null distribution). One caveat is that most people use "two-tailed" p-values, so you need to double the value you get from the above calculation...why? Because we assume our null is a normal distribution, hence it is symmetric about the mean, and therefore will have a lower tail area equal to the upper tail area.